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A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

Author

Listed:
  • Rabia Hameed
  • Ghulam Mustafa
  • Amina Liaqat
  • Dumitru Baleanu
  • Faheem Khan
  • Maysaa M. Al-Qurashi
  • Yu-Ming Chu

Abstract

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to continuity.

Suggested Citation

  • Rabia Hameed & Ghulam Mustafa & Amina Liaqat & Dumitru Baleanu & Faheem Khan & Maysaa M. Al-Qurashi & Yu-Ming Chu, 2020. "A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-17, October.
    • Handle: RePEc:hin:jnlmpe:6096545
    DOI: 10.1155/2020/6096545
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